We creat a 4 digit number greater than 5000 using the 0,1,3,5,7.What is the probability of creating a number divisible by 5 if the digits canot be repeated?Assume the numbers are randomly selected.
Answers
Answer:
Step-by-step explanation:
A 4 digit number greater than 5000 is randomly formed from digits 0,1,3,5,7.
(1) Repetition is allowed:
We need to form a number greater than 5000, hence, the leftmost digit can be either 5 or 7.
Since repetition of digits is allowed, so the remaining three places can be filled by 0,1,3,5,or7.
Hence, the total number of 4 digit numbers that can be formed greater than 5000 are = 2×5×5×5=250
But, we can’t count 5000 so the total number becomes 250–1=249.
The number is divisible by 5 only if the number at unit’s place is either 0or5.
Hence, the total number of numbers greater than 5000 and divisible by 5 are = 2×5×5×2 – 1 = 99
Hence, the required probability is given by =
249
99
=
83
33
.
(2) If repetition of digits is not allowed:
For a number to be greter than 5000, the digit at thousand’s place can be either 5 or 7.
The remaining three places can be filled by any of the four digits.
hence, total number of numbers greater than 5000= 2×4×3×2=48.
When the digit at thousand’s place is 5, units digit can be 0 and the tens and hundreds digit can be any two of the remaining three digits.
Hence, the number of 4 digit numbers starting with 5 and divisible by 5= 3×2=6
When the digit at thousand’s place is 7, units digit can be filled in two ways (0 or 5) and the tens and hundreds digit can be any two of the remaining three digits.
Hence, the number of 4 digit numbers starting with 7 and divisible by 5 = 1×2×3×2=12.
therefore, the number of 4 digit numbers greater than 5000 and divisible by 5=12+6=18
hence, the required probability =
48
18
=
8
3